Unless you are pressing the shutter button or whichever button you designated to activate the camera, there is no communication going on with the lens. It's just that simple. The cameras power switch may be in the on position but that doesn't mean the camera is active, it simply means power is available. Nothing is doing anything until you half press the shutter release or whatever button you have assigned that function to.
I have changed lenses on all of my Canon and Nikon DSLR'S with the power switch in the on position numerous times with absolutely no I'll effect. If anyone wants to turn the power off, that's absolutely fine.

A

If you remove the lens from your 5D3, you will notice a series of spring loaded contacts on the body that mate with the stationary contacts on the lens. Now when you initially mount the lens before rotating into the locked position, you’ll also notice that the flange of the lens is flush with the flange of the body. Soooo, when you rotate the lens into the locked position, each of the contacts on the lens touches each of the contacts in the body, but not until the lens is completely locked do all the contacts line up CORRECTLY. That means that as you rotate the lens the last contact patch on the lens touches the first contact on the body, and as you continue to rotate the lens until locked, it touches every contact before finally touching the correct contact when locked. Not only does this mean that almost every contact on the lens touches the WRONG contact at the body while rotating, but that the contacts on the lens MAY be able to bridge two adjoining contacts on the body. The only thing that MAY save you is if the camera automatically shuts off power to the lens within the first few degrees of rotation either way - locking or unlocking, and Canon MAY have built this in as a safety feature, but I’m certainly not risking my 5D3 on that possibility. But if you want to, feel free, but I think that’s bad advice for other owners unless you can document such a safety feature. If you cannot, the advice to shut off power BEFORE changing lenses stands, at least on EOS mount bodies and lenses.

Don't bother, UNLESS your manual instructs you to do so. I have never concerned myself with turning the camera off when swapping lenses because I didn't recall any such instruction in the manual that came with my camera (or the updates). Just as in the discussion of whether to power down while changing cards, it does not appear to be necessary.

I read all the responses until just before now (with time out to recheck the manual to my Canon 5D Mark III)--nowhere could I find a suggestion or direction to power down the camera to change lenses--I was pretty sure this would be the case when I started because I have read it several times and I am picky about complying with the instructions on use and care (I did break one of the rules--I dropped the camera a little over a month ago, but that was nothing I tried to do). Despite all of the statements of our UHH crowd, I see no reason to turn the power off to change lenses--none the reasons for doing so that have been offered in this thread are echoed in the manual from the manufacturer and none of the concerns are addressed as issues in the manual. I generally have little patience with proscriptions offered without a basis in actual knowledge--like those for obtaining permission to photograph in public places--and none of the reasoning here is discussed in the manual for my camera, not "the sensor is charged," the "contacts will rub and may spark," "any electronic device should be powered off to work with it," or any of the others. Of course, other cameras well may have such requirements--one should follow the instructions in the operator's/owner's manual.